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Use Simpson's Rule with $ n = 6 $ to estimate the length of the curve $ x = t - e^t $, $ -6 \leqslant t \leqslant 6 $.

$\begin{aligned} L &=\int_{a}^{b} \sqrt{1+\left(\frac{d}{d x}\right)^{2}} d x \\ L &=\int_{-6}^{6} \sqrt{1+\left(1-e^{*}\right)^{2}} d t \\ & \approx 407.13 \end{aligned}$

Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 2

Calculus with Parametric Curves

Parametric Equations

Polar Coordinates

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